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March 5, 2015 23:48
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import static java.lang.Math.atan; | |
import static java.lang.Math.cos; | |
import static java.lang.Math.sin; | |
public class FFT4g { | |
private int[] ip; | |
private double[] w; | |
private int n; | |
FFT4g(int n) { | |
this.n = n; | |
ip = new int[2+(int)Math.sqrt((double)n/2.0)+1]; | |
w = new double[n/2]; | |
ip[0] = 0; | |
} | |
public void rdft(int isgn, double[] a) | |
{ | |
int nw, nc; | |
double xi; | |
nw = ip[0]; | |
if (n > (nw << 2)) { | |
nw = n >> 2; | |
makewt(nw); | |
} | |
nc = ip[1]; | |
if (n > (nc << 2)) { | |
nc = n >> 2; | |
makect(nc, w, nw); | |
} | |
if (isgn >= 0) { | |
if (n > 4) { | |
bitrv2(n, a); | |
cftfsub(a); | |
rftfsub(a, nc, w, nw); | |
} else if (n == 4) { | |
cftfsub(a); | |
} | |
xi = a[0] - a[1]; | |
a[0] += a[1]; | |
a[1] = xi; | |
} else { | |
a[1] = 0.5 * (a[0] - a[1]); | |
a[0] -= a[1]; | |
if (n > 4) { | |
rftbsub(a, nc, w, nw); | |
bitrv2(n, a); | |
cftbsub(a); | |
} else if (n == 4) { | |
cftfsub(a); | |
} | |
} | |
} | |
private void makewt(int nw) | |
{ | |
int j, nwh; | |
double delta, x, y; | |
ip[0] = nw; | |
ip[1] = 1; | |
if (nw > 2) { | |
nwh = nw >> 1; | |
delta = atan(1.0) / nwh; | |
w[0] = 1; | |
w[1] = 0; | |
w[nwh] = cos(delta * nwh); | |
w[nwh + 1] = w[nwh]; | |
if (nwh > 2) { | |
for (j = 2; j < nwh; j += 2) { | |
x = cos(delta * j); | |
y = sin(delta * j); | |
w[j] = x; | |
w[j + 1] = y; | |
w[nw - j] = y; | |
w[nw - j + 1] = x; | |
} | |
bitrv2(nw, w); | |
} | |
} | |
} | |
void makect(int nc, double[] c, int nw) | |
{ | |
int j, nch; | |
double delta; | |
ip[1] = nc; | |
if (nc > 1) { | |
nch = nc >> 1; | |
delta = atan(1.0) / nch; | |
c[nw + 0] = cos(delta * nch); | |
c[nw + nch] = 0.5 * c[nw + 0]; | |
for (j = 1; j < nch; j++) { | |
c[nw + j] = 0.5 * cos(delta * j); | |
c[nw + nc - j] = 0.5 * sin(delta * j); | |
} | |
} | |
} | |
/* -------- child routines -------- */ | |
private void bitrv2(int n, double[] a) | |
{ | |
int j, j1, k, k1, l, m, m2; | |
double xr, xi, yr, yi; | |
ip[2 + 0] = 0; | |
l = n; | |
m = 1; | |
while ((m << 3) < l) { | |
l >>= 1; | |
for (j = 0; j < m; j++) { | |
ip[2 + m + j] = ip[2 + j] + l; | |
} | |
m <<= 1; | |
} | |
m2 = 2 * m; | |
if ((m << 3) == l) { | |
for (k = 0; k < m; k++) { | |
for (j = 0; j < k; j++) { | |
j1 = 2 * j + ip[2 + k]; | |
k1 = 2 * k + ip[2 + j]; | |
xr = a[j1]; | |
xi = a[j1 + 1]; | |
yr = a[k1]; | |
yi = a[k1 + 1]; | |
a[j1] = yr; | |
a[j1 + 1] = yi; | |
a[k1] = xr; | |
a[k1 + 1] = xi; | |
j1 += m2; | |
k1 += 2 * m2; | |
xr = a[j1]; | |
xi = a[j1 + 1]; | |
yr = a[k1]; | |
yi = a[k1 + 1]; | |
a[j1] = yr; | |
a[j1 + 1] = yi; | |
a[k1] = xr; | |
a[k1 + 1] = xi; | |
j1 += m2; | |
k1 -= m2; | |
xr = a[j1]; | |
xi = a[j1 + 1]; | |
yr = a[k1]; | |
yi = a[k1 + 1]; | |
a[j1] = yr; | |
a[j1 + 1] = yi; | |
a[k1] = xr; | |
a[k1 + 1] = xi; | |
j1 += m2; | |
k1 += 2 * m2; | |
xr = a[j1]; | |
xi = a[j1 + 1]; | |
yr = a[k1]; | |
yi = a[k1 + 1]; | |
a[j1] = yr; | |
a[j1 + 1] = yi; | |
a[k1] = xr; | |
a[k1 + 1] = xi; | |
} | |
j1 = 2 * k + m2 + ip[2 + k]; | |
k1 = j1 + m2; | |
xr = a[j1]; | |
xi = a[j1 + 1]; | |
yr = a[k1]; | |
yi = a[k1 + 1]; | |
a[j1] = yr; | |
a[j1 + 1] = yi; | |
a[k1] = xr; | |
a[k1 + 1] = xi; | |
} | |
} else { | |
for (k = 1; k < m; k++) { | |
for (j = 0; j < k; j++) { | |
j1 = 2 * j + ip[2 + k]; | |
k1 = 2 * k + ip[2 + j]; | |
xr = a[j1]; | |
xi = a[j1 + 1]; | |
yr = a[k1]; | |
yi = a[k1 + 1]; | |
a[j1] = yr; | |
a[j1 + 1] = yi; | |
a[k1] = xr; | |
a[k1 + 1] = xi; | |
j1 += m2; | |
k1 += m2; | |
xr = a[j1]; | |
xi = a[j1 + 1]; | |
yr = a[k1]; | |
yi = a[k1 + 1]; | |
a[j1] = yr; | |
a[j1 + 1] = yi; | |
a[k1] = xr; | |
a[k1 + 1] = xi; | |
} | |
} | |
} | |
} | |
private void rftfsub(double[] a, int nc, double[] c, int nw) | |
{ | |
int j, k, kk, ks, m; | |
double wkr, wki, xr, xi, yr, yi; | |
m = n >> 1; | |
ks = 2 * nc / m; | |
kk = 0; | |
for (j = 2; j < m; j += 2) { | |
k = n - j; | |
kk += ks; | |
wkr = 0.5 - c[nw + nc - kk]; | |
wki = c[nw + kk]; | |
xr = a[j] - a[k]; | |
xi = a[j + 1] + a[k + 1]; | |
yr = wkr * xr - wki * xi; | |
yi = wkr * xi + wki * xr; | |
a[j] -= yr; | |
a[j + 1] -= yi; | |
a[k] += yr; | |
a[k + 1] -= yi; | |
} | |
} | |
private void rftbsub(double[] a, int nc, double[] c, int nw) | |
{ | |
int j, k, kk, ks, m; | |
double wkr, wki, xr, xi, yr, yi; | |
a[1] = -a[1]; | |
m = n >> 1; | |
ks = 2 * nc / m; | |
kk = 0; | |
for (j = 2; j < m; j += 2) { | |
k = n - j; | |
kk += ks; | |
wkr = 0.5 - c[nw + nc - kk]; | |
wki = c[nw + kk]; | |
xr = a[j] - a[k]; | |
xi = a[j + 1] + a[k + 1]; | |
yr = wkr * xr + wki * xi; | |
yi = wkr * xi - wki * xr; | |
a[j] -= yr; | |
a[j + 1] = yi - a[j + 1]; | |
a[k] += yr; | |
a[k + 1] = yi - a[k + 1]; | |
} | |
a[m + 1] = -a[m + 1]; | |
} | |
private void cftfsub(double[] a) | |
{ | |
int j, j1, j2, j3, l; | |
double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i; | |
l = 2; | |
if (n > 8) { | |
cft1st(a); | |
l = 8; | |
while ((l << 2) < n) { | |
cftmdl(l, a); | |
l <<= 2; | |
} | |
} | |
if ((l << 2) == n) { | |
for (j = 0; j < l; j += 2) { | |
j1 = j + l; | |
j2 = j1 + l; | |
j3 = j2 + l; | |
x0r = a[j] + a[j1]; | |
x0i = a[j + 1] + a[j1 + 1]; | |
x1r = a[j] - a[j1]; | |
x1i = a[j + 1] - a[j1 + 1]; | |
x2r = a[j2] + a[j3]; | |
x2i = a[j2 + 1] + a[j3 + 1]; | |
x3r = a[j2] - a[j3]; | |
x3i = a[j2 + 1] - a[j3 + 1]; | |
a[j] = x0r + x2r; | |
a[j + 1] = x0i + x2i; | |
a[j2] = x0r - x2r; | |
a[j2 + 1] = x0i - x2i; | |
a[j1] = x1r - x3i; | |
a[j1 + 1] = x1i + x3r; | |
a[j3] = x1r + x3i; | |
a[j3 + 1] = x1i - x3r; | |
} | |
} else { | |
for (j = 0; j < l; j += 2) { | |
j1 = j + l; | |
x0r = a[j] - a[j1]; | |
x0i = a[j + 1] - a[j1 + 1]; | |
a[j] += a[j1]; | |
a[j + 1] += a[j1 + 1]; | |
a[j1] = x0r; | |
a[j1 + 1] = x0i; | |
} | |
} | |
} | |
private void cftbsub(double[] a) | |
{ | |
int j, j1, j2, j3, l; | |
double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i; | |
l = 2; | |
if (n > 8) { | |
cft1st(a); | |
l = 8; | |
while ((l << 2) < n) { | |
cftmdl(l, a); | |
l <<= 2; | |
} | |
} | |
if ((l << 2) == n) { | |
for (j = 0; j < l; j += 2) { | |
j1 = j + l; | |
j2 = j1 + l; | |
j3 = j2 + l; | |
x0r = a[j] + a[j1]; | |
x0i = -a[j + 1] - a[j1 + 1]; | |
x1r = a[j] - a[j1]; | |
x1i = -a[j + 1] + a[j1 + 1]; | |
x2r = a[j2] + a[j3]; | |
x2i = a[j2 + 1] + a[j3 + 1]; | |
x3r = a[j2] - a[j3]; | |
x3i = a[j2 + 1] - a[j3 + 1]; | |
a[j] = x0r + x2r; | |
a[j + 1] = x0i - x2i; | |
a[j2] = x0r - x2r; | |
a[j2 + 1] = x0i + x2i; | |
a[j1] = x1r - x3i; | |
a[j1 + 1] = x1i - x3r; | |
a[j3] = x1r + x3i; | |
a[j3 + 1] = x1i + x3r; | |
} | |
} else { | |
for (j = 0; j < l; j += 2) { | |
j1 = j + l; | |
x0r = a[j] - a[j1]; | |
x0i = -a[j + 1] + a[j1 + 1]; | |
a[j] += a[j1]; | |
a[j + 1] = -a[j + 1] - a[j1 + 1]; | |
a[j1] = x0r; | |
a[j1 + 1] = x0i; | |
} | |
} | |
} | |
private void cft1st(double[] a) | |
{ | |
int j, k1, k2; | |
double wk1r, wk1i, wk2r, wk2i, wk3r, wk3i; | |
double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i; | |
x0r = a[0] + a[2]; | |
x0i = a[1] + a[3]; | |
x1r = a[0] - a[2]; | |
x1i = a[1] - a[3]; | |
x2r = a[4] + a[6]; | |
x2i = a[5] + a[7]; | |
x3r = a[4] - a[6]; | |
x3i = a[5] - a[7]; | |
a[0] = x0r + x2r; | |
a[1] = x0i + x2i; | |
a[4] = x0r - x2r; | |
a[5] = x0i - x2i; | |
a[2] = x1r - x3i; | |
a[3] = x1i + x3r; | |
a[6] = x1r + x3i; | |
a[7] = x1i - x3r; | |
wk1r = w[2]; | |
x0r = a[8] + a[10]; | |
x0i = a[9] + a[11]; | |
x1r = a[8] - a[10]; | |
x1i = a[9] - a[11]; | |
x2r = a[12] + a[14]; | |
x2i = a[13] + a[15]; | |
x3r = a[12] - a[14]; | |
x3i = a[13] - a[15]; | |
a[8] = x0r + x2r; | |
a[9] = x0i + x2i; | |
a[12] = x2i - x0i; | |
a[13] = x0r - x2r; | |
x0r = x1r - x3i; | |
x0i = x1i + x3r; | |
a[10] = wk1r * (x0r - x0i); | |
a[11] = wk1r * (x0r + x0i); | |
x0r = x3i + x1r; | |
x0i = x3r - x1i; | |
a[14] = wk1r * (x0i - x0r); | |
a[15] = wk1r * (x0i + x0r); | |
k1 = 0; | |
for (j = 16; j < n; j += 16) { | |
k1 += 2; | |
k2 = 2 * k1; | |
wk2r = w[k1]; | |
wk2i = w[k1 + 1]; | |
wk1r = w[k2]; | |
wk1i = w[k2 + 1]; | |
wk3r = wk1r - 2 * wk2i * wk1i; | |
wk3i = 2 * wk2i * wk1r - wk1i; | |
x0r = a[j] + a[j + 2]; | |
x0i = a[j + 1] + a[j + 3]; | |
x1r = a[j] - a[j + 2]; | |
x1i = a[j + 1] - a[j + 3]; | |
x2r = a[j + 4] + a[j + 6]; | |
x2i = a[j + 5] + a[j + 7]; | |
x3r = a[j + 4] - a[j + 6]; | |
x3i = a[j + 5] - a[j + 7]; | |
a[j] = x0r + x2r; | |
a[j + 1] = x0i + x2i; | |
x0r -= x2r; | |
x0i -= x2i; | |
a[j + 4] = wk2r * x0r - wk2i * x0i; | |
a[j + 5] = wk2r * x0i + wk2i * x0r; | |
x0r = x1r - x3i; | |
x0i = x1i + x3r; | |
a[j + 2] = wk1r * x0r - wk1i * x0i; | |
a[j + 3] = wk1r * x0i + wk1i * x0r; | |
x0r = x1r + x3i; | |
x0i = x1i - x3r; | |
a[j + 6] = wk3r * x0r - wk3i * x0i; | |
a[j + 7] = wk3r * x0i + wk3i * x0r; | |
wk1r = w[k2 + 2]; | |
wk1i = w[k2 + 3]; | |
wk3r = wk1r - 2 * wk2r * wk1i; | |
wk3i = 2 * wk2r * wk1r - wk1i; | |
x0r = a[j + 8] + a[j + 10]; | |
x0i = a[j + 9] + a[j + 11]; | |
x1r = a[j + 8] - a[j + 10]; | |
x1i = a[j + 9] - a[j + 11]; | |
x2r = a[j + 12] + a[j + 14]; | |
x2i = a[j + 13] + a[j + 15]; | |
x3r = a[j + 12] - a[j + 14]; | |
x3i = a[j + 13] - a[j + 15]; | |
a[j + 8] = x0r + x2r; | |
a[j + 9] = x0i + x2i; | |
x0r -= x2r; | |
x0i -= x2i; | |
a[j + 12] = -wk2i * x0r - wk2r * x0i; | |
a[j + 13] = -wk2i * x0i + wk2r * x0r; | |
x0r = x1r - x3i; | |
x0i = x1i + x3r; | |
a[j + 10] = wk1r * x0r - wk1i * x0i; | |
a[j + 11] = wk1r * x0i + wk1i * x0r; | |
x0r = x1r + x3i; | |
x0i = x1i - x3r; | |
a[j + 14] = wk3r * x0r - wk3i * x0i; | |
a[j + 15] = wk3r * x0i + wk3i * x0r; | |
} | |
} | |
private void cftmdl(int l, double[] a) | |
{ | |
int j, j1, j2, j3, k, k1, k2, m, m2; | |
double wk1r, wk1i, wk2r, wk2i, wk3r, wk3i; | |
double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i; | |
m = l << 2; | |
for (j = 0; j < l; j += 2) { | |
j1 = j + l; | |
j2 = j1 + l; | |
j3 = j2 + l; | |
x0r = a[j] + a[j1]; | |
x0i = a[j + 1] + a[j1 + 1]; | |
x1r = a[j] - a[j1]; | |
x1i = a[j + 1] - a[j1 + 1]; | |
x2r = a[j2] + a[j3]; | |
x2i = a[j2 + 1] + a[j3 + 1]; | |
x3r = a[j2] - a[j3]; | |
x3i = a[j2 + 1] - a[j3 + 1]; | |
a[j] = x0r + x2r; | |
a[j + 1] = x0i + x2i; | |
a[j2] = x0r - x2r; | |
a[j2 + 1] = x0i - x2i; | |
a[j1] = x1r - x3i; | |
a[j1 + 1] = x1i + x3r; | |
a[j3] = x1r + x3i; | |
a[j3 + 1] = x1i - x3r; | |
} | |
wk1r = w[2]; | |
for (j = m; j < l + m; j += 2) { | |
j1 = j + l; | |
j2 = j1 + l; | |
j3 = j2 + l; | |
x0r = a[j] + a[j1]; | |
x0i = a[j + 1] + a[j1 + 1]; | |
x1r = a[j] - a[j1]; | |
x1i = a[j + 1] - a[j1 + 1]; | |
x2r = a[j2] + a[j3]; | |
x2i = a[j2 + 1] + a[j3 + 1]; | |
x3r = a[j2] - a[j3]; | |
x3i = a[j2 + 1] - a[j3 + 1]; | |
a[j] = x0r + x2r; | |
a[j + 1] = x0i + x2i; | |
a[j2] = x2i - x0i; | |
a[j2 + 1] = x0r - x2r; | |
x0r = x1r - x3i; | |
x0i = x1i + x3r; | |
a[j1] = wk1r * (x0r - x0i); | |
a[j1 + 1] = wk1r * (x0r + x0i); | |
x0r = x3i + x1r; | |
x0i = x3r - x1i; | |
a[j3] = wk1r * (x0i - x0r); | |
a[j3 + 1] = wk1r * (x0i + x0r); | |
} | |
k1 = 0; | |
m2 = 2 * m; | |
for (k = m2; k < n; k += m2) { | |
k1 += 2; | |
k2 = 2 * k1; | |
wk2r = w[k1]; | |
wk2i = w[k1 + 1]; | |
wk1r = w[k2]; | |
wk1i = w[k2 + 1]; | |
wk3r = wk1r - 2 * wk2i * wk1i; | |
wk3i = 2 * wk2i * wk1r - wk1i; | |
for (j = k; j < l + k; j += 2) { | |
j1 = j + l; | |
j2 = j1 + l; | |
j3 = j2 + l; | |
x0r = a[j] + a[j1]; | |
x0i = a[j + 1] + a[j1 + 1]; | |
x1r = a[j] - a[j1]; | |
x1i = a[j + 1] - a[j1 + 1]; | |
x2r = a[j2] + a[j3]; | |
x2i = a[j2 + 1] + a[j3 + 1]; | |
x3r = a[j2] - a[j3]; | |
x3i = a[j2 + 1] - a[j3 + 1]; | |
a[j] = x0r + x2r; | |
a[j + 1] = x0i + x2i; | |
x0r -= x2r; | |
x0i -= x2i; | |
a[j2] = wk2r * x0r - wk2i * x0i; | |
a[j2 + 1] = wk2r * x0i + wk2i * x0r; | |
x0r = x1r - x3i; | |
x0i = x1i + x3r; | |
a[j1] = wk1r * x0r - wk1i * x0i; | |
a[j1 + 1] = wk1r * x0i + wk1i * x0r; | |
x0r = x1r + x3i; | |
x0i = x1i - x3r; | |
a[j3] = wk3r * x0r - wk3i * x0i; | |
a[j3 + 1] = wk3r * x0i + wk3i * x0r; | |
} | |
wk1r = w[k2 + 2]; | |
wk1i = w[k2 + 3]; | |
wk3r = wk1r - 2 * wk2r * wk1i; | |
wk3i = 2 * wk2r * wk1r - wk1i; | |
for (j = k + m; j < l + (k + m); j += 2) { | |
j1 = j + l; | |
j2 = j1 + l; | |
j3 = j2 + l; | |
x0r = a[j] + a[j1]; | |
x0i = a[j + 1] + a[j1 + 1]; | |
x1r = a[j] - a[j1]; | |
x1i = a[j + 1] - a[j1 + 1]; | |
x2r = a[j2] + a[j3]; | |
x2i = a[j2 + 1] + a[j3 + 1]; | |
x3r = a[j2] - a[j3]; | |
x3i = a[j2 + 1] - a[j3 + 1]; | |
a[j] = x0r + x2r; | |
a[j + 1] = x0i + x2i; | |
x0r -= x2r; | |
x0i -= x2i; | |
a[j2] = -wk2i * x0r - wk2r * x0i; | |
a[j2 + 1] = -wk2i * x0i + wk2r * x0r; | |
x0r = x1r - x3i; | |
x0i = x1i + x3r; | |
a[j1] = wk1r * x0r - wk1i * x0i; | |
a[j1 + 1] = wk1r * x0i + wk1i * x0r; | |
x0r = x1r + x3i; | |
x0i = x1i - x3r; | |
a[j3] = wk3r * x0r - wk3i * x0i; | |
a[j3 + 1] = wk3r * x0i + wk3i * x0r; | |
} | |
} | |
} | |
} |
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